Ssamacheer Kalvi Math Solution for Exercise 3.15 Part2

This page samacheer kalvi math solution for exercise 3.15 part2 is going to provide you solution for every problems that you find in the exercise no 3.15

Samacheer Kalvi Math Solution for Exercise 3.15 part2

(v)  x² - ( √3 + 1) x + √3 = 0

Solution:

x = -1 , -√3

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(2) Solve the following quadratic equations using quadratic formula 

(i) x²- 7x + 12 = 0

Solution:

  a = 1     b = -7    c = 12

             = 8/2, 6/2

             = 4, 3

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(ii) 15x²- 11 x + 2 = 0

Solution:

          a = 15   b = - 11     c = 2

          = 12/30 ,   10/30

          = 2/5 , 1/3

In the page samacheer kalvi math solution for exercise 3.15 part1  we are going to see the solution of next problem

(iii) x + (1/x) = 2 ½

Solution:

             (x² + 1)/x = 5/2

          2 (x² + 1) = 5 x

          2 x² + 2 = 5 x 

          2 x² - 5 x + 2 = 0

      a = 2       b = -5      c = 2

 x = 8/4 , 2/4

 x = 2 , 1/2

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(iv) 3 a²x² - ab x - 2b² = 0

       a = 3 a²   b = - ab   c = - 2b²

x = 6ab/6a²  , -4ab/6a²

x = b/a , x = -2b/a

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(v) a (x² + 1) =  x(a² + 1)

Solution:

      a x² + a =  x(a² + 1)

      a x² - x(a² + 1) + a = 0

a = a     b = -(a² + 1)   c = a      

        x = 2a²/2a , 2/2a

           = a , 1/a 

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(vi) 36 x² - 12 a x + (a² - b²) =  0

  a = 36        b = -12 a      c = (a² - b²)

           x = (a + b)/6 , (a - b)/6

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(vii) [(x - 1)/(x + 1)] + [(x - 3)/(x - 4)] = 10/3

 Solution:

     [(x - 1)(x - 4) + (x - 3)(x + 1)]/(x + 1)(x- 4) = 10/3

     (x² - 5 x + 4 + x² - 2 x - 3)/(x² - 3 x - 4) = 10/3

  3 (2x² - 7 x + 1) = 10(x² - 3 x - 4)

  10 x² - 6 x² - 30 x + 21 x - 40 - 3 = 0

  4 x² - 9 x - 43 = 0

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(viii) a² x² + (a²- b²)x - b²= 0

Solution:

 a = a²     b = (a²- b²)         c = - b²

x = 2b²/2a², -2a²/2a²

x = b²/a² , -1